This question may appear brief, but I think it is simple enough to not need much background. Basically, I'm curious about the nature of God and His desires. Does He want things? What are some of the things He wants, and how did we find out about these things?

Citations from specific literature (Bible or otherwise) where you have evidence of His wants would be particularly helpful. :-)

Here is a passage that answers the question even if it also perplexes me:

James 4:5 (ESV)
Or do you suppose it is to no purpose that the Scripture says, "He yearns jealously over the spirit that he has made to dwell in us"?

Looks like God really wants us to come back to him. I don't understand why it's said this way, nor do I know what scripture James is referring to but it does seem clear that one thing he wants from us is that we abide in Him!

God wants to be glorified by His creatures. In the Lord's prayer, the first statement we make is "Our Father who art in heaven, hallowed by thy name." When Moses was appealing to God for the fate of the Israelis, he used the point that He would get disrepute if He killed them. God repented. (Ex.32:11-14)

God wants us to do listen to his voice, or that is obey him. He wants us to learn about him and his qualities. He wants us to try to reflect his qualities as best we can.

Lastly he wants us to recognize his position and power. We are also his witness that Satan the devil is a liar. These are the only "things" that we can give back to god. What material things can we give god that he doesn't already have or can create? Acts 7:48-50

"However, the Most High does not dwell in houses made with hands, just as the prophet says: 49 ‘The heaven is my throne and the earth is my footstool. What sort of house will you build for me? Jehovah says. Or where is my resting-place? 50 My hand made all these things, did it not?"

God has us give him our material things, but this is not because God needs them. Rather he is looking to see by our actions how much we love him.

Also he wants this to be done only in one specific place in Jerusalem: Deuteronomy 12:11.

As the sole place of Jewish sacrifice (Deuteronomy 12), the Temple replaced the portable sanctuary (aka The Tabernacle) constructed in the Sinai Desert under the auspices of Moses, as well as local sanctuaries, and altars in the hills.